# steps 4,5, 6 use euclidean distance
library(plotly)
library(seriation)
Question 1.
# keep columns 1,2,5,6,7,9,10,16,17,18,19
p_e <- prices_earnings[, c(1,2,5,6,7,9,10,16,17,18,19)]
rownames(p_e) <- p_e[[1]]
Question 2.
Without doing any reordering We cannot identify any clusters or outliers.
#p_e_sc %>%
plot_ly(x =~colnames(p_e_sc), y =~rownames(p_e_sc),
z = ~p_e_sc, type = "heatmap",
colors = colorRamp(c("black","red"))
) %>%
layout(title = "Heatmap of prices and earnings",
xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
yaxis = list(title = "Cities", zeroline = FALSE)
)
Question 3.
# seriation needs to permute rows and columns, thus distance by row and column
p_e_rdist <- dist(p_e_sc, method = "euclidean")
p_e_cdist <- dist(t(p_e_sc), method = "euclidean")
# make sure that results are reproducible
#set.seed(1011)
# get orders of the row and col distances; Hamilton path length
order1 <- get_order(seriate(p_e_rdist, method = "OLO"))
order2 <-get_order(seriate(p_e_cdist, method = "OLO"))
p_reord <- p_e_sc[rev(order1), order2]
plot_ly(x =~colnames(p_reord), y =~rownames(p_reord),
z = ~p_reord, type = "heatmap",
colors = colorRamp(c("black","red"))
) %>%
layout(title = "Heatmap of prices and earnings (Euclid dist - HC)",
xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
yaxis = list(title = "Cities", zeroline = FALSE)
)
# computing distance as one minus correlation
p_e_cor <- as.dist((1 - cor(p_e_sc))/2)
p_e_cor1 <- as.dist((1 - cor(t(p_e_sc)))/2)
# set seed to ensure results are reproducible
#set.seed(1212)
# get orders for columns and rows
ord1 <- get_order(seriate(p_e_cor, method = "OLO"))
ord2 <- get_order(seriate(p_e_cor1, method = "OLO"))
# reorder
p_reord2 <- p_e_sc[rev(ord2), ord1]
plot_ly(x =~colnames(p_reord2), y =~rownames(p_reord2),
z = ~p_reord2, type = "heatmap",
colors = colorRamp(c("black","red"))
) %>%
layout(title = "Heatmap of prices and earnings (Cor dist)",
xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
yaxis = list(title = "Cities", zeroline = FALSE)
)
The ordering by euclidean distance produces a heat map that is easier to analyze. At first glance we can perceive four general regions of two groups. The first group heat map color tends towards a brighter shade of red while the second group tend towards a darker shade of red/black. Although these groups can be seen in the correlation distance heat map, it is not as clear as the first.
Based on the euclidean distance heat map, net wage tends to higher values from Dubai while the number of hours worked decrease. This is the opposite to cities like Delhi,Bankok and Seoul. Interestingly food costs are generally low in the cities with highee working hours. Caracas is an outlier because food costs are high while net wage and the number of hours worked remains low.
Question 4.
# use p_e_rdist and p_e_cdist (euclidean distance)
ord_q4_1 <- get_order(seriate(p_e_rdist, method = "TSP"))
order_q4_2 <-get_order(seriate(p_e_cdist, method = "TSP"))
p_reord_q4 <- p_e_sc[rev(ord_q4_1), order_q4_2]
plot_ly(x =~colnames(p_reord_q4), y =~rownames(p_reord_q4),
z = ~p_reord_q4, type = "heatmap",
colors = colorRamp(c("black","red"))
) %>%
layout(title = "Heatmap of prices and earnings (Euclid dist- TSP)",
xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
yaxis = list(title = "Cities", zeroline = FALSE)
)
# function creterion to compare unordered distance and ordered
# distance = p_e_rdist (row distance)
# or = order
or1 <- seriate(p_e_rdist, method = "OLO")
or2 <- seriate(p_e_rdist, method = "TSP")
result1 <- rbind(unordered = criterion(p_e_rdist), ordered = criterion(p_e_rdist,or1 ))
result2 <- rbind(unordered = criterion(p_e_rdist), ordered = criterion(p_e_rdist,or2 ))
result1
2SUM AR_deviations AR_events BAR Cor_R Gradient_raw Gradient_weighted Inertia
unordered 1012004.5 107139.67 61656 29259.38 0.04268063 -4032 -11081.08 17886336
ordered 756120.2 20296.15 26876 19055.56 0.20713342 65528 156151.06 24666913
Lazy_path_length Least_squares LS ME Moore_stress Neumann_stress Path_length RGAR
unordered 10126.431 3575435 1006126.8 568.2673 986.9925 553.9889 281.7269 0.5169014
ordered 3713.804 3352459 894638.7 652.4429 411.5392 239.0233 121.9671 0.2253186
result2
2SUM AR_deviations AR_events BAR Cor_R Gradient_raw Gradient_weighted Inertia
unordered 1012004.5 107139.67 61656 29259.38 0.04268063 -4032 -11081.08 17886336
ordered 853587.1 49156.93 42860 20469.13 0.11525856 33560 93357.18 21965231
Lazy_path_length Least_squares LS ME Moore_stress Neumann_stress Path_length RGAR
unordered 10126.431 3575435 1006126.8 568.2673 986.9925 553.9889 281.7269 0.5169014
ordered 4695.498 3436184 936501.3 650.3093 426.3088 243.1948 119.8891 0.3593226
TSP solver has shorter path length compared to HC solver.
Question 5.
# parallel coordinates plot from unsorted scaled data
p_e_sc2 <- as.data.frame(p_e_sc)
p_e_sc2 <- round(p_e_sc2, 1)
p_e_sc2 %>% plot_ly(type ="parcoords",
dimensions = list(
list(label = "Food.Costs...", values = ~Food.Costs...),
list(label = "iPhone.4S.hr.", values = ~iPhone.4S.hr.),
list(label = "Clothing.Index", values = ~Clothing.Index),
list(label = "Hours.Worked", values = ~Hours.Worked),
list(label = "Wage.Net", values = ~Wage.Net),
list(label = "Vacation.Days", values = ~Vacation.Days),
list(label = "Big.Mac.min.", values = ~Big.Mac.min.),
list(label = "Bread.kg.in.min.", values = ~Bread.kg.in.min.),
list(label = "Rice.kg.in.min.", values = ~Rice.kg.in.min.),
list(label = "Goods.and.Services...", values = ~Goods.and.Services...)
)
)
# adding a factored column by iphone column which defines the clusters
p_e_sc2$clust <-ifelse(p_e_sc2$iPhone.4S.hr. < -0.5, 0, 1)
p_e_sc2 %>% plot_ly(type ="parcoords",
line = list(color = ~clust, colorscale = list(c(0, "red"), c(1, "blue"))),
dimensions = list(
list(label = "Food.Costs...", values = ~Food.Costs...),
list(label = "iPhone.4S.hr.", values = ~iPhone.4S.hr.),
list(label = "Clothing.Index", values = ~Clothing.Index),
list(label = "Hours.Worked", values = ~Hours.Worked),
list(label = "Wage.Net", values = ~Wage.Net),
list(label = "Vacation.Days", values = ~Vacation.Days),
list(label = "Big.Mac.min.", values = ~Big.Mac.min.),
list(label = "Bread.kg.in.min.", values = ~Bread.kg.in.min.),
list(label = "Rice.kg.in.min.", values = ~Rice.kg.in.min.),
list(label = "Goods.and.Services...", values = ~Goods.and.Services...)
)
)
We can identify two clusters defined by Wage net (blue) and iphone 4s (red). Wage net has values greater than 0 in the red cluster (defined by iphone 4) while iphone has values has values greater than -0.5 in the blue cluster.
---
title: "Visualization Lab 3"
author: "Roshni Sundaramurthy (rossu809) & Brian Masinde (brima748)"
date: "26 September 2018"
output:
  html_document:
    df_print: paged
  html_notebook:
    theme: journal
  pdf_document: default
fontsize: 11pt
bibliography: references.bib
---

```{r message=FALSE, warning=FALSE, paged.print=FALSE}
# steps 4,5, 6 use euclidean distance
library(plotly)
library(seriation)
```

```{r data, echo = FALSE}
prices_earnings <- read.delim("prices-and-earnings.txt")
```
### Question 1.
```{r}
# keep columns 1,2,5,6,7,9,10,16,17,18,19

p_e <- prices_earnings[, c(1,2,5,6,7,9,10,16,17,18,19)]

rownames(p_e) <- p_e[[1]]
```

```{r scale, echo = FALSE}
# question 2 scaling
p_e_sc <- scale(p_e[,-1])

```

### Question 2.
Without doing any reordering We cannot identify any clusters or outliers.

```{r heatmap}
#p_e_sc %>% 
  plot_ly(x =~colnames(p_e_sc), y =~rownames(p_e_sc),
    z = ~p_e_sc, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings",
         xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )
```

### Question 3.

```{r question3_a_dist}
# seriation needs to permute rows and columns, thus distance by row and column
p_e_rdist <- dist(p_e_sc, method = "euclidean")

p_e_cdist <- dist(t(p_e_sc), method = "euclidean")
```

```{r question3_a_order}
# make sure that results are reproducible
#set.seed(1011)
# get orders of the row and col distances; Hamilton path length
order1 <- get_order(seriate(p_e_rdist, method = "OLO"))

order2 <-get_order(seriate(p_e_cdist, method = "OLO"))

p_reord <- p_e_sc[rev(order1), order2]
```

```{r question3_a_heat}
plot_ly(x =~colnames(p_reord), y =~rownames(p_reord),
    z = ~p_reord, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings (Euclid dist - HC)",
         xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )
```


```{r question3_b_dist}
# computing distance as one minus correlation

p_e_cor <- as.dist((1 - cor(p_e_sc))/2)

p_e_cor1 <- as.dist((1 - cor(t(p_e_sc)))/2)
```

```{r question3_b_order}
# set seed to ensure results are reproducible
#set.seed(1212)

# get orders for columns and rows
ord1 <- get_order(seriate(p_e_cor, method = "OLO"))

ord2 <- get_order(seriate(p_e_cor1, method = "OLO"))

# reorder
p_reord2 <- p_e_sc[rev(ord2), ord1]
```


```{r question3_b_heat}
plot_ly(x =~colnames(p_reord2), y =~rownames(p_reord2),
    z = ~p_reord2, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings (Cor dist)",
         xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )
```

The ordering by euclidean distance produces a heat map that is easier to analyze. At first glance we can perceive four general regions of two groups. The first group heat map color tends towards a brighter shade of red while the second group tend towards a darker shade of red/black. Although these groups can be seen in the correlation distance heat map, it is not as clear as the first.

Based on the euclidean distance heat map, net wage tends to higher values from Dubai while the number of hours worked decrease. This is the opposite to cities like Delhi,Bankok and Seoul. Interestingly food costs are generally low in the cities with highee working hours. Caracas is an outlier because food costs are high while net wage and the number of hours worked remains low.


### Question 4.
```{r question4_order}
# use p_e_rdist and p_e_cdist (euclidean distance)
ord_q4_1 <- get_order(seriate(p_e_rdist, method = "TSP"))

order_q4_2 <-get_order(seriate(p_e_cdist, method = "TSP"))

p_reord_q4 <- p_e_sc[rev(ord_q4_1), order_q4_2]
```

```{r question4_heat}
plot_ly(x =~colnames(p_reord_q4), y =~rownames(p_reord_q4),
    z = ~p_reord_q4, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings (Euclid dist- TSP)",
         xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )
```

```{r question4_crit}
# function creterion to compare unordered distance and ordered
# distance = p_e_rdist (row distance)
# or = order
or1 <- seriate(p_e_rdist, method = "OLO")

or2 <- seriate(p_e_rdist, method = "TSP")

result1 <- rbind(unordered = criterion(p_e_rdist), ordered = criterion(p_e_rdist,or1 ))

result2 <- rbind(unordered = criterion(p_e_rdist), ordered = criterion(p_e_rdist,or2 ))
```

```{r question4_crit1}
result1
```

```{r question4_crit2}
result2
```

TSP solver has shorter path length compared to HC solver.

### Question 5.

```{r}
# parallel coordinates plot from unsorted scaled data 

p_e_sc2 <- as.data.frame(p_e_sc)

p_e_sc2 <- round(p_e_sc2, 1)

```


```{r parcoord, fig.width= 9.5, fig.height=8}
p_e_sc2 %>% plot_ly(type ="parcoords",
  dimensions = list(
    list(label = "Food.Costs...", values = ~Food.Costs...),
    list(label = "iPhone.4S.hr.", values = ~iPhone.4S.hr.),
    list(label = "Clothing.Index", values = ~Clothing.Index),
    list(label = "Hours.Worked", values = ~Hours.Worked),
    list(label = "Wage.Net", values = ~Wage.Net),
    list(label = "Vacation.Days", values = ~Vacation.Days),
    list(label = "Big.Mac.min.", values = ~Big.Mac.min.),
    list(label = "Bread.kg.in.min.", values = ~Bread.kg.in.min.),
    list(label = "Rice.kg.in.min.", values = ~Rice.kg.in.min.),
    list(label = "Goods.and.Services...", values = ~Goods.and.Services...)
  )
)
```


```{r}
# adding a factored column by iphone column which defines the clusters
p_e_sc2$clust <-ifelse(p_e_sc2$iPhone.4S.hr. < -0.5, 0, 1)
 
```

```{r}
p_e_sc2 %>% plot_ly(type ="parcoords",
  line = list(color = ~clust, colorscale = list(c(0, "red"), c(1, "blue"))),
  dimensions = list(
    list(label = "Food.Costs...", values = ~Food.Costs...),
    list(label = "iPhone.4S.hr.", values = ~iPhone.4S.hr.),
    list(label = "Clothing.Index", values = ~Clothing.Index),
    list(label = "Hours.Worked", values = ~Hours.Worked),
    list(label = "Wage.Net", values = ~Wage.Net),
    list(label = "Vacation.Days", values = ~Vacation.Days),
    list(label = "Big.Mac.min.", values = ~Big.Mac.min.),
    list(label = "Bread.kg.in.min.", values = ~Bread.kg.in.min.),
    list(label = "Rice.kg.in.min.", values = ~Rice.kg.in.min.),
    list(label = "Goods.and.Services...", values = ~Goods.and.Services...)
  )
)
```

We can identify two clusters defined by Wage net (blue) and iphone 4s (red). Wage net has values greater than 0 in the red cluster (defined by iphone 4) while iphone has values has values greater than -0.5 in the blue cluster.